Hom Functor: Abelian Groups

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Related lectures (54)

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Active Learning Session Log in to Mediaspace to watch this video

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Group Homomorphisms Log in to Mediaspace to watch this video

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Introduction to Category Theory: Functors Log in to Mediaspace to watch this video

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Introduction to Category Theory: Adjoint Functors Log in to Mediaspace to watch this video

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

Equivalences of Categories Log in to Mediaspace to watch this video

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Group Actions and Functors Log in to Mediaspace to watch this video

Covers group quotient, group actions, and functors connecting sets and G-sets.

Motivations for studying group actions Log in to Mediaspace to watch this video

Covers group actions, bijections, evaluations, translations, homomorphisms, and inverses within universal actions.

Homotopical Algebra: Examples and Adjunctions Log in to Mediaspace to watch this video

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

Endomorphisms: Matrix Equivalence Log in to Mediaspace to watch this video

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

Galois Theory: Solvability and Radical Extensions Log in to Mediaspace to watch this video

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Orbital and Fixed Point Functors Log in to Mediaspace to watch this video

Formalizes the construction of orbits and fixed points in group actions, defining morphisms and verifying naturalness.

Linear Representations: Basics and Examples Log in to Mediaspace to watch this video

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

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